This invention relates to investigation of earth formation and, more particularly, to a method and apparatus for determining properties of earth formations using sonic well logging with multiwave processing.
It is well known that mechanical disturbances can be used to establish acoustic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear and Stoneley waves, such as their velocity (or its inverse, slowness) in the formation and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources.
An example of a logging device that has been used to obtain and analyze sonic logging measurements of formations surrounding an earth borehole is called a Dipole Shear Sonic Imager (xe2x80x9cDSTxe2x80x9dxe2x80x94trademark of Schlumberger) and is of the type described in Harrison et al., xe2x80x9cAcquisition and Analysis of Sonic Waveforms From a Borehole Monopole And Dipole Source For The Determination Of compressional And Shear Speeds And Their Relation To Rock Mechanical Properties And Surface Seismic Dataxe2x80x9d, Society of Petroleum Engineers, SPE 20557, 1990.
Commercial sonic logging tool processing techniques conventionally xe2x80x9cwindowxe2x80x9d the acquired sonic waveforms. [For description of other prior logging techniques using sonic arrays, and approaches in which windowing of acquired waveforms has been used, see, for example, Kimball, C. V., and Marzetta, T. L., xe2x80x9cSemblance Processing Of Borehole Acoustic Array Data, Geophysics, 49, pp. 274-281, 1986; U.S. Pat. Nos. 4,594,691; 5,278,805; and Esmersoy, C., Koster, K., Williams, M., Boyd, A., and Kane, M., xe2x80x9cDipole Shear Anisotropy Loggingxe2x80x9d, 60-th Ann. Internet. Mtg., Soc. Explor. Geophys., Expanded Abstracts. pp. 1139-1142, 1994.] The windowing procedure employs a time window of selected duration that is judiciously positioned to separate a desired wave from other waveform components because the subsequent processing is valid only for particular single wave types. Positioning the window has always been a problem because the output estimates depend significantly on window position. To believe an estimate, one must believe the window is positioned properly. In practice, window positions are often untenable from a physical point of view. Moreover, windowing is known to introduce bias in the measurement (see Parks, T. W., Morris, C. F., and Ingram, J. D., xe2x80x9cVelocity Estimation From Short-Time Temporal And Spatial Frequency Estimatesxe2x80x9d, Proc. of ICASSP, pp. 399-402, 1992).
Multiwave processing, that is, processing multiple waves jointly, offers advantages in many situations, particularly when the wave model includes tool arrivals. [See Esmersoy, C., xe2x80x9cInversion Of P And SV Waves From Multicomponent Offset Vertical Seismic Profilesxe2x80x9d, Geophysics, January 1990; Kimball, C. V., Lewicki, P. and Wijeyesekera, N., xe2x80x9cError Analysis Of Maximum Likelihood Estimates From One or More Dispersive Wavesxe2x80x9d, IEEE Trans. On Signal Processing, 43, No. 12, pp. 2928-2936, 1995.] Recent multiwave processing approaches are described, for example, in Kimball, C. V., xe2x80x9cShear Slowness Measurement By Dispersive Processing Of The Borehole Flexural Mode, Geophysics, 63, pp. 337-344, 1998; and U.S. Pat. No. 5,687,138. Although multiwave processing is intended to process more than one wave (i.e., wave type), the intended number of waves is usually less than the number of waves actually present in the logging data. Moreover, performance in estimating formation characteristics can tend to decrease as the number of waves included in the processing increases, so more waves in the model doesn""t of itself lead to better estimates.
It is among the objects of the present invention to provide an improved multiwave processing technique and apparatus that overcomes shortcomings of prior art approaches, including the limitations of existing windowing processing.
Applicant has discovered that by redefining the underlying signal model, multiwave processing can attain the benefits of windowing without the uncertainties of window positioning and without bias. This permits application of least mean square estimation (xe2x80x9cLMSExe2x80x9d) without the need to resort to ad hoc techniques.
In accordance with an embodiment of the invention, a method is set forth for determining acoustic properties, such as compressional wave slowness and shear wave slowness, of earth formations surrounding a borehole, comprising the following steps: (a) transmitting acoustic energy from a transmitter location and receiving acoustic energy at a plurality of receiver locations in the borehole, at least a portion of the received acoustic energy having travelled through the formations; (b) deriving data signals from the acoustic energy received at the receiver locations; (c) selecting model values of the acoustic properties; (d) producing an intermediate matrix that is a function of a window matrix, the window matrix being a function of at least one of the model values; (e) performing a singular value decomposition on the intermediate matrix to obtain a basis matrix of eigenvectors; (f) deriving a propagator matrix as a function of the model values; (g) producing a reduced propagator matrix from the propagator matrix and the basis matrix; (h) producing a test statistic using the data signals and the reduced propagator matrix; (i) repeating steps (c) through (h) for different combinations of model values, and selecting, as output acoustic property values, the combination of model values that results in a maximized test statistic.
In a preferred embodiment of the invention, the steps (d), (e), and (f) are each performed for a plurality of different wave types (e.g. compressional waves, shear waves, Stoneley waves, and flexural waves). Also in this embodiment, the step (e) further includes truncating said eigenvectors of the basis matrix to produce a reduced basis matrix, and the step (g) comprises producing the reduced propagator matrix from the propagator matrix and the reduced basis matrix. Also in this embodiment, the step (d) of producing an intermediate matrix comprises producing an intermediate matrix that is also a function of a filter matrix. The window matrix is a time domain matrix and said filter matrix is a frequency domain matrix, and the intermediate matrix is formed by transforming the window matrix to the frequency domain, implementing filtering on the transformed window matrix, and transforming the result to the time domain.
The multiwave processing of the present invention offers potential advantages in many well logging applications. Some examples of these are: so-called labelling-free monopole compressional, shear, and Stoneley processing (without the need for long transmitter-to-receiver spacings to have labelled windowed arrivals); centralized and eccentered Stoneley/flexural wave processing (processing in situations where eccentering or tool imperfections result in waves other than pure flexural waves, such as Stoneley waves, that would ordinarily make it more difficult to invert for shear slowness); fast and slow shear processing in anisotropic formations; and combinations of the above, with or without the presence of so-called tool arrivals of waves that propagate through the logging tool itself. Reference an can be made, for example, to C. Esmersoy, Inversion Of P And SV Waves From Multicomponent Offset Vertical Seismic Profiles, Geophysics, January, 1990; C. V. Kimball et al., Error Analysis Of Maximum Likelihood Estimates From One Or More Dispersive Waves, IEEE Trans. On Signal Processing, 43, No. 12, pp. 2928-2936, 1995; U.S. Pat. Nos. 5,687,138; and 5,808,963.
Further features and advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings.